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research article

Distributionally Robust Convex Optimization

Wiesemann, Wolfram
•
Kuhn, Daniel  
•
Sim, Melvyn
2014
Operations Research

Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker's prior information. In this paper, we propose a unifying framework for modeling and solving distributionally robust optimization problems. We introduce standardized ambiguity sets that contain all distributions with prescribed conic representable confidence sets and with mean values residing on an affine manifold. These ambiguity sets are highly expressive and encompass many ambiguity sets from the recent literature as special cases. They also allow us to characterize distributional families in terms of several classical and/or robust statistical indicators that have not yet been studied in the context of robust optimization. We determine sharp conditions under which distributionally robust optimization problems based on our standardized ambiguity sets are computationally tractable. We also provide tractable conservative approximations for problems that violate these conditions.

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Type
research article
DOI
10.1287/opre.2014.1314
Author(s)
Wiesemann, Wolfram
Kuhn, Daniel  
Sim, Melvyn
Date Issued

2014

Published in
Operations Research
Volume

62

Issue

6

Start page

1358

End page

1376

Subjects

Robust optimization

•

Ambiguous probability distributions

•

Conic optimization

Note

Available from Optimization Online

URL

URL

http://www.optimization-online.org/DB_HTML/2013/02/3757.html
Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
RAO  
Available on Infoscience
January 22, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/100100
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